Answer
$\begin{array}{ c c }
a) & \mathrm{Choice\ }\mathbf{C}\\
b) & \mathrm{Choice\ }\mathbf{D}\\
c) & \mathrm{Choice\ }\mathbf{D}\\
d) & \mathrm{Choice\ }\mathbf{C}
\end{array}$
Work Step by Step
$\begin{array}{|c|l|}
\hline
a) & \begin{array}{l}
\mathrm{Recall\ the\ exponent\ rule\ } a^{-b} \ =\ \dfrac{1}{a^{b}} .\ \\
\mathrm{Apply\ the\ rule\ for\ case\ a) :}\\
=\dfrac{1}{5^{3}} =\dfrac{1}{( 5)( 5)( 5)} =\dfrac{1}{125} \ \mathrm{which\ matches\ Choice\ }\mathbf{C.} \
\end{array}\\
& \\
\hline
b) & \begin{array}{l}
\mathrm{For\ case\ b}) :\\
=-\dfrac{1}{5^{3}} =-\dfrac{1}{( 5)( 5)( 5)} =-\dfrac{1}{125} \ \mathrm{which\ matches\ Choice\ }\mathbf{D} .
\end{array}\\
& \\
\hline
c) & \begin{array}{l}
\mathrm{For\ case\ c}) :\ \\
\dfrac{1}{( -5)^{3}} =\dfrac{1}{( -5)( -5)( -5)} =\dfrac{1}{-125} =-\dfrac{1}{125}\\
\mathrm{which\ matches\ Choice\ }\mathbf{D} .
\end{array}\\
& \\
\hline
d) & \begin{array}{l}
\mathrm{For\ case\ d) :}\\
-\dfrac{1}{( -5)^{3}} =-\dfrac{1}{( -5)( -5)( -5)} =-\dfrac{1}{-125} =-\left( -\dfrac{1}{125}\right) =\dfrac{1}{125}\\
\mathrm{which\ matches\ Choice\ }\mathbf{C} .
\end{array}\\
\hline
\end{array}$
